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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

Semiclosed operators in Hilbert space


Author: William E. Kaufman
Journal: Proc. Amer. Math. Soc. 76 (1979), 67-73
MSC: Primary 47A05
MathSciNet review: 534392
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Abstract: In a Hilbert space H, an operator C is semiclosed provided that there exists a bounded operator B on H, with range the domain of C, such that CB is bounded. The family of all such operators in H is the smallest family containing all closed operators and itself closed under any one of the following: (1) sums, (2) products, (3) strong limits on domains of closed operators. In fact, every algebraic combination of closed operators in H is the sum of two closed one-to-one operators with the same domain and closed ranges.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1979-0534392-9
PII: S 0002-9939(1979)0534392-9
Keywords: Closed operator, semiclosed operator, Hilbert space, complete inner product space, operator ranges
Article copyright: © Copyright 1979 American Mathematical Society